Aluminium Design and Construction - Chapter 12 ppt

CHAPTER 12

Fatigue
12.1 GENERAL DESCRIPTION
It is well known that seemingly ductile metal components can fail in a
brittle manner at a low load, far below their static strength, when this
load is applied many times. Aluminium is more prone to this problem
than steel.
The phenomenon, known as fatigue, results from the presence of
localized details or irregularities in zones carrying tensile stress, especially
at welds. These act as stress-raisers and although they have no effect on
static resistance, they become critical under repeated load. Elastic analysis
predicts a peak stress at such positions that greatly exceeds the basic
stress found using conventional stress formulae. The ratio of peak to
basic stress, the stress-concentration factor, can reach a value of 3 or
more. The peak stress, which is highly localized, causes a microscopic
crack to form (‘initiate’) at a relatively low level of basic stress, which
then grows (‘propagates’) each time the load is applied. At first the rate
of propagation per load cycle is minute, but after many cycles it speeds
up, eventually leading to catastrophic failure.
In non-welded construction, a fatigue crack may form at a bolt or
rivet hole, at a sudden change of cross-section, or at any other geometric
irregularity. Just the very slight surface roughness of the aluminium
itself, well away from any joint or change of section, may be sufficient
to cause fatigue. Welded components fare worse. Even when the welding
is to the highest standard, there are still inevitable stress-raisers at the
toe or root of a weld, and also in the ripples on the weld surface. These
all lead to an inferior performance in fatigue. With lower standards of
fabrication, the welds are likely to contain additional unintended defects
(micro-cracks, undercut, lack of penetration), which will reduce the
fatigue strength still further. The level of inspection specified to the

fabricator can be crucial.
The number of cycles N to failure (the endurance) at a given detail is
found to relate mainly to the stress range (f
r
), especially for cracks initiating
at welds. In other words, what matters is the difference between maximum
and minimum stress in each cycle. Modern design rules for fatigue are
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
therefore usually presented in terms of f
r
and ignore any slight influence
that the mean stress might have.
Surprisingly, the choice of alloy has little effect on fatigue performance
of members and the rules in current codes relate equally to all aluminium
materials. Fatigue therefore becomes more critical with the stronger
alloys, which are likely to operate at higher levels of stress in service.
The critical factor is the severity of the stress-raiser or defect. For example,
if a cover plate is welded to the flange of an extruded beam, the stress
range at the extreme fibres for a given fatigue life (say, 2 million cycles)
may be reduced by 60%. Or, putting it another way, the anticipated life
for a given range of extreme fibre stress might typically decrease by a
factor of 30. Two other effects that can influence fatigue performance are:
• Corrosion fatigue. There is likely to be an added risk of fatigue failure
if the structure has to operate in a very corrosive environment.
• Scale effect. For any given form of detail geometry, tests show that a
thick component will be more prone to fatigue failure than a thin one.
A useful rough rule is to take the fatigue strength (limiting value of f
r
)
of an aluminium detail, for a given number of cycles, as one-third of

that for a similar detail in steel. The fatigue data in BS.8118 aims to be
more accurate than this and provides nine endurance curves of stress
range f
r
plotted against endurance N which are specific to aluminium.
These are intended to cover most likely classes of detail, and are based
on a large experimental programme using life-size specimens. These
curves are generally more favourable than ‘steel ÷ 3’, especially at the
high endurance/ low f
r
end.
The simplest situation is when the load cycles are of known and
constant amplitude, as for a member supporting vibrating machinery.
More often, there is a load spectrum comprising loads of varying amplitude
and frequency, or even random loading. Often the most difficult problem
in fatigue assessment is to estimate and then rationalize the pattern of
the loading.
It is vital to identify the various types of loading that could lead to
possible fatigue failure. These include:
• moving loads;
• vibration from machinery;
• inertia effects in moving structures;
• environmental loading (wind, wave);
• forces due to repeated pressurization;
• forces due to repeated temperature change.
There have been many instances of failure where the possibility of fatigue
had not occurred to the designer. The author remembers the structure
of a building in which a long aluminium tension member suffered failure
even before the building had been clad. In service there was no possibility
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.

of fatigue, but the member had a low natural frequency of vibration
and, in the unclad condition, wind-excited oscillations caused it to fail
by flexural fatigue after a few weeks.
Another non-obvious type of fatigue failure is that due to transverse
stressing at the welds in slender plate-girders. If the web operates in
the post-buckled condition, due to a very high d/t ratio, it will flex in
and out each time the load is applied, causing repeated flexure about
the axis of the web/flange joint and hence fatigue in the weld.
The treatment of fatigue presented in this chapter is based on that in
BS.8118, which was largely the work of Ogle and Maddox [30] at the
TWI. The data provided for welded details refers specifically to arc-
welded joints (MIG, TIG). Friction-stir welding is still in its infancy, but
preliminary results suggest the FS process produces joints which are
much better in fatigue than those made by MIG or TIG.
12.2 POSSIBLE WAYS OF HANDLING FATIGUE
There are three possible approaches for checking a proposed design
against failure by fatigue:
1. safe life method;
2. fail-safe method (‘damage-tolerant’ approach);
3. testing.
The usual method (1), which is entirely done by calculation, is the one
explained in this chapter. It essentially consists of estimating the range
of stress f
r
, arising in service at any critical position, finding the
corresponding endurance N from the relevant f
r
-N curve, and then
checking that the resulting life is not less than that required.
In method (2), the safety margins in design are lower than those

required in a safe-life design. This is permissible because regular inspection
is carried out, enabling the growth of any fatigue cracks to be monitored
during the life of the structure. If the size of a crack or the rate of crack
growth exceeds that allowed, the structure is taken out of service and
the critical component repaired or replaced. Obviously, it is essential
that all potential fatigue sites should be easily inspectable if this method
is to be adopted, and considerable expertise is needed. Inspection methods,
the time between inspections, acceptable crack lengths and allowable
rates of crack growth must all be agreed between the designer and the
user of the structure. When fatigue is critical, the fail-safe method will
tend to produce a lighter structure than method (1). It is the approach
most used in aircraft design. British Standard BS.8118 does not cover
the fail-safe method, and it is beyond the scope of this book.
Fatigue testing (3) should be employed when it is impossible to apply
method (1), due to problems in verifying a design by calculation alone.
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
For example:
• The loading spectrum is unknown and cannot be reliably calculated.
• The geometry of the structure makes stress-analysis difficult.
• It is not clear to which fatigue class a certain detail should be assigned.
Testing may also be preferred even when method (1) would be possible.
For example with a mass-produced component, built to closely controlled
standards of workmanship, it may be found that fatigue testing of
prototypes would indicate a better performance than that predicted
from the standard endurance curves. Advice on fatigue testing appears
in BS.8118.
12.3 CHECKING PROCEDURE (SAFE LIFE)
12.3.1 Constant amplitude loading
The simplest type of fatigue calculation is when a single load is repeatedly
applied to the structure, so that at any point there is a steady progression

from minimum to maximum stress in each cycle without any intervening
blips (Figure 12.1), referred to as constant amplitude loading. In such a
case, the checking procedure at each potential fatigue site is as follows:
1. Decide on the design life of the structure. Refer to Section 12.3.3.
2. Calculate the number of load cycles n during the design life.
3. Determine the pattern and variation of nominal (unfactored) loading
on the structure in each cycle.
4. Calculate the resulting stress range (f
r
) at the position being considered
—generally taken as the difference between maximum and minimum
stress in each cycle. Refer to Sections 12.3.4 and 12.4.
5. Establish the class of the detail at the point considered. Refer to
Section 12.5.
6. Using the endurance-curve appropriate to the class, read off the
predicted number of cycles to failure (N) corresponding to the stress
range f
r
. Refer to Section 12.6.
7. The fatigue resistance at the point considered is acceptable if N
у
n.
Figure 12.1 Constant amplitude loading. f
r
=stress range, f
m
=mean stress.
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12.3.2 Variable amplitude loading
The simple state of affairs covered in Section 12.3.1 is fairly rare. In

most fatigue situations, the loading is more complex, leading to a spectrum
of stress ranges at any critical position. This is known as variable amplitude
loading and the checking procedure runs as follows:
1. Decide on the design life of the structure, referring to Section 12.3.3
as before.
2. Find the number of load cycles during the design life.
3. Obtain the variation of nominal unfactored stress f in each cycle at
the point considered (Figure 12.2). Refer to Sections 12.3.4 and 12.4.
4. Rationalize this stress history by reducing it to a set of specific stress
ranges (f
r1
, f
r2
, f
r3
, etc.), the number of times that each occurs during
the design life being denoted by n
1
, n
2
, n
3
, etc. This provides a stress
range spectrum (Section 12.3.5).
5. Establish the class of the detail at the point considered. Refer to
Section 12.5.
6. Select the appropriate endurance curve, and for each stress range
value (f
r1
, f

r2
, f
r3
, etc.) read off the corresponding endurance (N
1
, N
2
,
N
3
, etc.) that would be achieved if that stress range were the only
one acting. Refer to Section 12.6.
7. The fatigue resistance at the point considered is acceptable if the
Palmgren-Miner rule is satisfied:
(12.1)
12.3.3 Design life
The nominal design life of a structure is the time for which it is expected
to be in service, and this should be agreed with the client. British Standard
BS.8118 gives a range of typical values for a variety of applications.
The design life, as used in fatigue calculations, is normally taken the
same as the nominal design life. However, the British Standard gives a
designer the option of playing safer, if thought necessary, by multiplying
the nominal life by a fatigue life factor
L
(>1). A decision to do this would
hinge on the accuracy of the assumed loading spectrum, whether records
of loading will be kept, or the possibility of a change in use during the
structure’s life. It is fairly rare to step up the design life in this way.
12.3.4 Stress range
The stress range (f

r
) is normally taken equal to the nominal stress range,
namely the range over which f varies when nominal (unfactored) loads
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
act on the structure. However, BS.8118 gives a designer the option to
increase f
r
by multiplying the nominal stress range by a factor
mf
(>1).
This might be felt advisable if: (a) the structure will have to operate in
a very corrosive environment: or (b) failure at the position considered
would result in total collapse, i.e. there is no alternative load path. In
practise, it is fairly unusual to take
mf
> 1.
British Standard BS.8118 allows a relaxation when f ranges from f
t
tensile to f
c
compressive, in which case the compressive component
may be reduced by 40%. In other words, we then take f
r
=f
t
+0.6f
c
.
12.3.5 Stress-range spectrum
With variable amplitude loading, an essential step is to obtain the different

stress ranges (f
r1
, f
r2
, etc.) in each cycle, and one possible procedure for
so doing is the ‘reservoir’ method described in BS.8118. Referring to
Figure 12.2, the graph showing the variation of f during the cycle is
regarded as a reservoir, in which the greatest depth of water gives the
value f
r1.
The reservoir is then drained from its lowest point, the deepest
remaining pocket (or pockets) giving the value f
r2
. The process is repeated
until all the water has been drained, thus obtaining f
r3
, f
r4
, etc. This
enables a stress-range spectrum to be plotted, as shown in Figure 12.3.
This method is suitable when there is a sequence of loading events
repeated many times. An alternative procedure is the ‘rain-flow’ method
described in BS.5400: Part 10 (Steel, Concrete and Composite Bridges),
which is more convenient when long and variable stress histories have
to be analysed.
Figure 12.2 Variable amplitude loading, ‘reservoir’ method.
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12.4 REPRESENTATIVE STRESS
In determining the stress range (or stress-range spectrum) at a given
fatigue site, it is important to know just what stress (f) we are talking

about. There are essentially two methods (A, B) for defining f, the choice
of which depends on the nature of the detail and the manner in which
the crack propagates (Figure 12.4). Table 12.1 shows which method to
use when.
12.4.1 Method A
In this method, f is taken as the major principal stress at the point of
initiation, generally obtained by means of a simple analysis using
conventional expressions such as P/A, My/I, etc., based on the gross
cross-section without any reduction due to HAZ or local buckling effects.
Local stress concentrations as at a small hole or the toe of a weld are
ignored, this being justified by the use of a suitably lowered endurance
curve that takes account of them.
Figure 12.3 Stress-range spectrum.
Table 12.1 Choice of method for determining the representative stress f
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Larger geometrical effects receive a modified treatment whereby the
basic stress is multiplied by a stress concentration factor K, enabling a
higher endurance curve to be used. The factor K may be found from the
literature, or else by means of a finite element analysis. For a member
containing a large circular hole, we can generally take K=2.4, while at a
radiused change of section (Figure 12.5), K can be read from the curves
Figure 12.4 Crack propagation: (a) at non-welded details; (b) through parent metal at a
weld; (c) through weld metal.
Figure 12.5 Stress concentration factor K at a radiused change of section.
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
provided, to which the equation is (valid for a > r):
0.1 < r/b < 1 K=1.2 {1+ (1-e
-0.7a/r
)(1-r/b)
2

}
r/b > 1 K=1.2 (12.2)
Other non-linear effects which become significant in fatigue are the
secondary stresses in trusses, due to joint fixity, and the effects of shear
lag, distortion and warping in plated structures. The increased stress
levels resulting from these must be allowed for.
12.4.2 Method B
This is used for fillets and partial penetration butt welds transmitting
load from one plate to another. A notional value is assumed for f obtained
as follows:

(12.3)

where F
–
=force transmitted per unit length of joint at the position
considered, g=nominal throat dimension (Figure 11.7), and n=number
of welds.
Here F
–
can be a force transverse to the weld, a longitudinal one, or
a vectorial sum of the two. It is normally found in the same general
way as for P
–
when considering static resistance (Section 11.3.3), except
that we are now considering the force transmitted under nominal, and
not factored loading.
When a single weld suffers bending about its longitudinal axis, f should
be taken as the elastic flexural stress at the root, based on a linear stress
distribution through the (nominal) throat. If necessary, this component of

f should be added vectorially to the value found using equation (12.3).
Table 12.2 Classification of fatigue details (non-welded)
Notes. 1. Use K for cases 2, 3, 4.
2. An open hole having d/t in the range 2–3 may be treated as either case 4 (using actual stress
concentration factor K), or case 5 (putting K=1).
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12.5 CLASSIFICATION OF DETAILS
12.5.1 The BS.8118 classification
An essential step in any fatigue calculation is to classify the form of the
detail at the position being considered, so that the relevant endurance
curve can be selected. British Standard BS.8118 distinguishes nine such
classes, the reference number for each being the value of f
r
(in N/mm2
)
corresponding to a predicted endurance (N) of 2 million cycles. The
class numbers thus defined are 60, 50, 42, 35, 29, 24, 20, 17, 14.
The class for a given detail may be found by referring to the relevant
table, based on BS.8118:
Table 12.2 non-welded details;
Table 12.3 welded details, crack propagation through parent metal;
Table 12.4 welded details, crack propagation through the weld.
Table 12.3 Classification of fatigue details (arc-welded) —propagation through parent metal
Notes. 1. For cases 26–30, avoid weld returns around lap.
2. l=length of connected part in direction of f
r
.
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For details not covered in these tables the reader may refer to the more
comprehensive data provided in the British Standard.

The classes given in Tables 12.3 and 12.4 specifically refer to arc-
welded joints made by MIG or TIG. They will only be valid if the
fabrication meets a specified standard referred to in BS.8118 as ‘fatigue-
quality welding’ (Section 12.7).
12.5.2 Friction-stir welds
At the time of writing, the new friction-stir process is being actively
developed, and there are strong indications that FS welds will prove
far superior in fatigue to those made by MIG or TIG. For example, a
preliminary series of fatigue tests made by Hydro-Aluminium in Norway
on transverse butt welds in 6082-T4 extruded material, 5 mm thick,
suggest that class 50 might be appropriate for such a joint. This compares
with class 24 for a single-V MIG weld with permanent backing bar, or
class 17 if unbacked.
The reason for the better fatigue performance of FS welds is their flat
as-welded profile. To obtain optimum results, it is important to avoid
the small fin that can occur at the flow-zone edge of the nugget, when
the welding parameters are not properly controlled. Provided this fin
is eliminated, it is claimed that a fatigue class equal to 90% of that for
the parent metal is possible.
12.5.3 Bonded joints
Bonded joints are generally superior to welded ones in fatigue. Consider
first the performance of a member containing a longitudinal bonded joint,
Table 12.4 Classification of fatigue details (arc-welded) —propagation through weld
Notes. 1. For cases 34–37 the ends of the weld must be ground flush, using run-on and run-off plates.
2. For case 35 the class depends on how closely the weld profile is controlled (i.e. preventing
the use of excessive reinforcement).
3. For case 35 any change in thickness or width must be gradual, with tan р 0.25.
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
i.e. a joint extending in the same direction as the applied stress, as for the
web/flange connection in a beam. For such a joint, it is reasonable to

assume that there is little adverse effect due to the presence of the adhesive,
and take a class approaching that for the basic wrought metal (class 60).
Secondly, consider the case when fatigue loading acts transverse to
a bonded joint. Here there are two possibilities: tensile failure in the
aluminium, and shear failure in the adhesive. The former can be handled
in the same way as if the component were monolithic (no joint), taking
due account of the stress concentration caused by the geometry. The
latter is more difficult, due to lack of generally available data, and
testing becomes necessary.
12.6 ENDURANCE CURVES
British Standard BS.8118 provides endurance curves in the form of
stress range f
r
plotted against endurance N (number of cycles to failure),
covering the nine classes of fatigue detail. These are presented on a
log-log plot, where they appear as a series of straight lines, the general
form being shown diagramatically in Figure 12.6. Different curves are
provided for constant and variable amplitude loading:
1. Constant amplitude curves. For any given class, line A is defined by
the class number (=f
r
in N/mm
2
at N=2×10
6
) and the reverse gradient
1/m (as specified in Table 12.5). This line continues down to a horizontal
cut-off at N=10
7.
2. Variable amplitude curves. For a given class, this uses the same line A,

but only down to N=5×10
6
. There is then a transition line B of reverse
gradient 1/(m+2) going from N=5×10
6
to 10
8
, followed by a (lower)
horizontal cut-off.
For any given class, the equations to lines A and B are as follows, where
the values of kA and k
B
appear in Table 12.5:

(12.4a)

(12.4b)

Also given in the table are the cut-off values (f
oc
and f
ov
) for each class,
the idea being that a repeated stress range of lower magnitude is non-
damaging. The variable amplitude case has a lower cut-off, because
occasional stress ranges occurring above f
oc
will produce some propagation,
thus causing lower stress ranges to become damaging.
The resulting BS.8118 endurance curves are presented in Figure 12.7.

Comparison of these with certain European data might suggest that at
high N the British Standard endurance curves for welded details are too
low. In fact, it would be wrong to conclude that the British Standard is
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
wrong, since the height of the curves in this range is critically affected
by the standard of welding. The BS.8118 clearly states that the required
quality of production welds must be easily achievable and assurable.
12.7 INSTRUCTIONS TO FABRICATOR
In order that the class of a welded detail (as given in Table 12.3 or 12.4)
may be valid, the designer must specify fatigue-quality welding and
state the necessary level of inspection (Section 3.3.5). The drawings
should be marked with a ‘Fat-number’, giving the required class, and
also an arrow showing the direction of the stress fluctuation.
The predicted endurance of a welded detail based on its normal
classification will sometimes greatly exceed that actually needed, as
Table 12.5 Endurance curve parameters
Note. Stresses (f) are in N/mm
2
.
Figure 12.6 Construction of the endurance curves. C=constant amplitude loading,
V=variable amplitude.
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
when the design life is low or when a detail occurs in a zone of low
stress. For such a detail, it is possible to calculate the required class,
defined as the class of the lowest endurance curve that would produce
the required life. By specifying this class instead of the normal (maximum
possible) one for the detail considered, it becomes acceptable to relax
the inspection requirements and hence save money. British Standard
BS.8118 suggests the following procedure:
1. Determine those regions of the structure where the required class is

equal to or higher than class 24.
2. At all details in such regions, the Fat-number shown on the drawing
should indicate the required class, rather than the maximum possible
class.
3. The fabricator then tailors his level of inspection to the Fat-number
actually indicated.

An obvious example of where it is pointless to put the maximum possible
Fat-number on the drawing is when a potentially high-class detail occurs
adjacent to one of lower class. In such a case, the high-class detail may
be marked with the same Fat-number as that for the low-class one next
door to it, with nothing lost.
12.8 IMPROVEMENT MEASURES
If a critical detail fails to satisfy its fatigue check, the designer has
essentially two options. One is to increase the section, thus reducing
the level of stress. This increases weight and cost, and may be highly
inconvenient if the design is far advanced. The alternative is to carry
out an improvement measure, thus raising the fatigue class of the detail.
The following are some of the possibilities:
1. Redesign the detail. The original low-class detail is replaced by one of
higher class.
2. Weld-toe grinding. Grinding the toe of a transverse weld to a smooth
profile reduces the stress-concentration effect. If the crack is toe initiated,
the resistance to fatigue will be enhanced.
3. Weld-toe peening. Peening at the toe of a transverse weld introduces
compressive residual stress, which again improves the performance
when initiation is at the toe.
4. Cold expansion of a bolt hole, using a suitable drift. Like (3), this is helpful
because it produces compressive residual stress at the point needed.
5. Static overload. Another way of introducing beneficial compressive

residual stresses at potential fatigue sites is to give the whole
component a controlled static overload to a stress beyond the elastic
limit.
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
Figure 12.7 Fatigue endurance curves for aluminium. C=constant amplitude loading,
V=variable amplitude.
Copyright 1999 by Taylor & Francis Group. All Rights Reserved.
Methods (2) and (3) are difficult to control, and one would normally
resort to them only if fatigue problems had come to light during fabrication
or even in service. Method (4) probably falls in the same category,
although it is more controllable. Method (5) is a more reliable technique,
provided the application of the overload is properly specified, and can
be incorporated into the design. Methods (2) to (5) all require validation
by testing.
12.9 FATIGUE OF BOLTS
12.9.1 Basic approach
Fatigue checks should also be made on any bolts the structure may
contain, if these have to carry repeated tension. The root of a thread
acts as a severe stress-raiser, causing bolts to perform poorly in fatigue.
The first rule when fatigue is a factor is to avoid using bolts made of
aluminium, because of the metal’s intrinsic weakness in fatigue. The
following approach therefore focuses on steel bolts, for which the checking
procedure is the same as that used for checking a member, except in
two aspects, namely, the appropriate endurance curve and the
determination of the stress range. British Standard BS.8118 fails to give
guidance on the fatigue of bolts used in aluminium structures.
12.9.2 Endurance curves for steel bolts
Aluminium designers can make use of the fatigue data for steel bolts
provided in Part 10 of BS.5400 (Steel, Concrete and Composite Bridges).
This may be expressed in the form of conventional endurance curves,

as shown in Figure 12.8, the equations to which are as follows:

(12.5a)


(12.5b)

where: N=number of cycles to failure (with constant amplitude loading),
f
u
=ultimate strength of bolt material, and f
r
=range through which the
stress (f) varies.
The curves are radically different from those for members in that the
strength of the material is now a factor. They are valid for steel bolts
com-plying with BS.4395 (HSFG) or BS.3692 (Precision Bolts). They may
also be used for black bolts (BS.4190), provided these are faced under
the head and turned on the shank.

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When fatigue needs to be checked for stainless steel bolts, used in an
aluminium structure, it is suggested that the same endurance curves
may be employed as those provided for ordinary steel ones, in view of
the lack of readily available curves specific to stainless steel. This
suggestion is believed to be valid if the bolts have rolled threads, but
not necessarily with cut threads.
12.9.3 Variation of bolt tension
Figure 12.9 shows the typical variation in bolt tension T with the force T
1

,
defined as the applied force (per bolt) tending to pull the components
apart. If the bolt were done up finger-tight, we would have T=T
1
all the
way (line 1). If, however, the bolt is tightened to an initial preload T
0
, the
response will at first follow line 2, until separation occurs at C, after which

Figure 12.8 Endurance curves for steel bolts.
Figure 12.9 Variation of bolt tension T with applied external force T
1
.
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it reverts to line 1. The slope s of line 2 depends on the relative axial
stiffnesses of the bolt and the clamped plate material. Fisher and Struik
suggest that for all-steel construction s lies in the range 0.05–0.10. This
tallies with a statement made in Part 10 of BS.5400: “The increase in
tension will rarely exceed 10% of an external load”.
When a steel bolt is used with aluminium plates, the slope of line 2
will be greater, because of the lower modulus of the plate material (one
third). Extrapolating from Fisher and Struik’s figures for steel/steel
[33], a simple calculation suggests that s will now lie in the approximate
range 0.14–0.25. Thus a reasonable upper-bound approach for the steel/
aluminium case is to take:
T=0.25 T
1
(12.6)
where T

1
=change in T
1,
T=corresponding change in T.
It is suggested that the determination of the tensile stress range f
r
for
steel bolts used in aluminium structures should be based on T as
given by this equation. The fluctuation in bolt tension is seen to be
more severe than for all-steel construction.
Figure 12.9 illustrates the importance of doing a bolt up tight when
fatigue is a factor. If it were only tightened to a low initial tension,
causing plate separation to occur in service, it would pick up the full
fluctuation in the external force T
1
(shown as T in the figure) instead
of s times this. The range of variation in bolt tension would therefore
be increased, possibly quadrupled, with a drastic effect on the fatigue
life of the bolt.
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